AMD GCN 1 mobile cards in blender
I have the same GPU, and older versions of Blender support it. I think 2.78 was the last version to support this GPU generation. I don't know if there is some way to make new versions work with it.
Edit: Yes, 2.78 is the last version to support GCN 1.0 GPUs for Cycles rendering. From the 2.79 release notes:

Due to various issues with drivers for AMD GCN 1.0 architecture, those cards are no longer supported for Cycles rendering

You might not see a big improvement over rendering with your CPU though; this GPU isn't that powerful after all. I made a quick comparison between my CPU and GPU:

CPU (i5-6200U) took 8:13.03 with 4 threads rendering 48x48 blocks
each
GPU took 9:53.98 with 512x512 blocks, which actually got split
up into two 256x512 blocks by Blender because of some GPU memory limitation

You might get better results compared to your CPU, but just don't expect a lot from it.